How to determine when to approximate

[carlee_romero_3A]

I am confused about when is the proper time to determine when to approximate and when to use quadratic formula.

[Jenny Dis1D]

The benchmark value is 10^-3, so you can approximate when the x value is deemed too small aka 10^-3 or less.

[Alex Caracalla 1I]

In acid/base problems, is generally ok to approximate when the concentration of the acid/base is roughly 1000 (or 10^3) times greater than the given Ka/Kb value. If that is the case, then you can usually assume that the x value you are solving for is negligible compared to the concentration of your acid and won’t affect your calculation that much when you remove it from the denominator. Once you calculate x, you can verify your assumption by dividing it by the acid’s concentration, then multiplying by 100. If the % you get is greater than 5%, then your assumption was wrong and you need to go back and redo your calcs using the quadratic formula.

[Brandon_G_1H]

Hello! We usually approximate when the value of Ka or Kb isn’t in between 10^-3 and 10^3. Hope this helps!

[janice]

You can approximate the X value when K is less than 10^-4, for anything larger than that you will need to use the quadratic formula.

[005999765]

You can approximate when the value of X is too small which is at 10^-3 or less. Anything higher than this would need the quadratic formula.

[Sydney Tanimitsu 2B]

You can approximate when K is less than 10^-3, we can approximate since K is very small, and estimating wouldn't change the result. You can always double-check by using the 5% rule. This is when you approximate and then take the concentration that you would find and then divide it by the initial concentration if it is greater than 5% then the approximation is invalid and you will need to solve it without approximating but if it is less than 5% then the approximation is valid. When the 5% rule invalidates the approximation or K is greater than 10^-3 then you will need to use the quadratic equation to solve

[Andres Ibarra 2F]

You can approximate the x value when the K is less than 10^-4. It's usually when the value of Ka or Kb isn't between 10^-3 and !0^3. If it's larger then you would use the quadratic formula.

[Dalia Torres 3I]

Hi!

So this is a part of the 5% rule! You are supposed to approximate if K is extremely small; usually the cutoff value is 10^-3 or less than 5% (5% rule) of the initial concentration. I had this question too and it's okay to approximate because k is so small that it would not make too much of a difference to approximate!! Hope this helps!

[Tyler Olson 1E]

You can approximate when the Ka value is less than 10^-4 but after you achieve that value you need to check and it is only valid if it is less than 5% of the initial concentration. If it is bigger than that then you need to go back and do it without approximating.

[Reynaldo Fernandez 3L]

Any value of K that is less than 10^-3 is valid to approximate. This means that the concentration of the reactants is way higher than the equilibrium constant, which also means that it is higher than the concentration of the products at equilibrium. The reaction will always move forward if the reactant concentration is higher than the equilibrium constant, and the product concentration will be very low compared to the reactant concentration. The product that is produced won't have a big impact on the concentration of the reactants, so for any K value that is smaller than 10^-3, you can safely assume that the reactant concentration is way higher than the product concentration and use the approximation and not the quadratic equation.

[Jude Marting 2l]

When you solve for K and find it is equal to 10^-3 or smaller you can approximate. Dr. Lavelle in class compared it to a millionaire losing a thousand dollars they would still consider themselves a millionaire. It is the same for this, the value is so small it does not change the number significantly. So, if the value is 10^-3 or even smaller you can decide to skip the quadratic formula. It is totally up to you though and would save you time if you were pressed for it on the test while still getting the same answer.

[Emily_Hanna_2E]

Hey Carlee!
When you have a concentration-x or concentration-2x, etc you can drop the variable if you K value is less than 10^-3. Usually, this value will be in the denominator. So, say you have x^2/0.0065-x and your Ka or Kb value is 2*10^-6, you can drop the -x and solve in terms of x^2/0.0065 = 2*10^-6. You can also make sure that this is valid by finding the percent composition which is x/initial concentration *100. If it is less than 5%, the approximation works. Hope this was helpful!

[jadon_seow_3F]

The choice between using the quadratic formula or making an approximation depends on the size of the equilibrium constant and the initial concentrations of the reactants and products. When K is very small (<10^-3 I believe) and the initial concentrations of the reactants and products are significantly different, you can use the approximation method. This is because the change in concentration of the reactants and products during the reaction is negligible. On the other hand, when K is relatively large (>10^3), and the reaction has proceeded to a significant extent, you should use the quadratic formula. This is because the change in concentration of the reactants and products during the reaction cannot be neglected.